The EE% of 50% is dictating that you use 13.75# of grain to reach your OG target. A water ratio of 1.25 qt per pound leads to the 17.19 qts in mash. 13# and 17 qts would be pushing a 5-gal vessel.
You could reduce the water ratio and make it (barely) fit, but you can see the constraints of trying to do any brews with higher OGs.
When I pursued this path, I originally mashed the maximum pounds (~7#) that I could sparge in a pasta strainer I had, and then added DME to reach the OG target. Then I realized I could go all-grain if I would accept smaller batches of about 3.25 final volume. So, if you're committed to making 5.0 gallons of final volume, then you could either mash your maximum and add some extract, or buy bigger equipment if you want AG and 5 gals.
If you can accept small batches, you could do AG with current equipment. I did this, so I could learn about AG methods while gradually assembling bigger outdoor equipment. Any of these options will make fine beer.